I'm not sure if there's a way to refill your coolant without getting a ship upgrade, but it's super annoying to have to deal with half coolant for potentially quite a while (until you can save enough to buy an upgrade & get an upgrade unit).
I think perhaps offering a "full repair" at planets with an upgrade station that doesn't require an upgrade unit would be good, as it would still be a financial drain of sorts but could fix annoying issues like that, maybe refuel the engines to a neat 100% (instead of having them stuck at 95% and never being completely full), and just generally serve as a way to come back from a series of really bad collisions.
Eventually I lost all of my health so I stopped worrying about stamina, and honestly I had more fun when I just wasn't thinking about it. I would vote for its removal, but implementing eating (which isn't implemented as far as I can tell?) along with the hydroponics bay being a potential steady source of food would be a way to reward players for the first few upgrades.
Also, the collisions in asteroid fields seemed very frequent, to the point of sometimes having multiple in a row that necessitated at least half a health bar of excess work.
Finally, the computer says sleeping restores stamina & passes time, and while I notice it does restore stamina faster I don't notice it passing time faster? Maybe I'm just not very perceptive, though.